Limit properties of Luce's choice theory

Luce's Axiom is interpreted in terms of a sequence of measures on the unit interval, and their limit properties are discussed. In particular, all limit laws are found to be either absolutely continuous with density x^α for α ∈ (?1, ∞) or else degenerate laws consisting of a point mass at 0 or 1. A close connection between Luce's choice theory and Karamata's theory of regularly varying functions is established and systematically used.